Problem: Recently you have bought a snow walking robot and brought it home. Suppose your home is a cell (0, 0) on an infinite grid.

You also have the sequence of instructions of this robot. It is written as the string s consisting of characters 'L', 'R', 'U' and 'D'. If the robot is in the cell (x, y) right now, he can move to one of the adjacent cells (depending on the current instruction).

  * If the current instruction is 'L', then the robot can move to the left to (x - 1, y); 
  * if the current instruction is 'R', then the robot can move to the right to (x + 1, y); 
  * if the current instruction is 'U', then the robot can move to the top to (x, y + 1); 
  * if the current instruction is 'D', then the robot can move to the bottom to (x, y - 1). 



You've noticed the warning on the last page of the manual: if the robot visits some cell (except (0, 0)) twice then it breaks.

So the sequence of instructions is valid if the robot starts in the cell (0, 0), performs the given instructions, visits no cell other than (0, 0) two or more times and ends the path in the cell (0, 0). Also cell (0, 0) should be visited at most two times: at the beginning and at the end (if the path is empty then it is visited only once). For example, the following sequences of instructions are considered valid: "UD", "RL", "UUURULLDDDDLDDRRUU", and the following are considered invalid: "U" (the endpoint is not (0, 0)) and "UUDD" (the cell (0, 1) is visited twice).

The initial sequence of instructions, however, might be not valid. You don't want your robot to break so you decided to reprogram it in the following way: you will remove some (possibly, all or none) instructions from the initial sequence of instructions, then rearrange the remaining instructions as you wish and turn on your robot to move. 

Your task is to remove as few instructions from the initial sequence as possible and rearrange the remaining ones so that the sequence is valid. Report the valid sequence of the maximum length you can obtain.

Note that you can choose any order of remaining instructions (you don't need to minimize the number of swaps or any other similar metric).

You have to answer q independent test cases.

Input

The first line of the input contains one integer q (1 ≤ q ≤ 2 ⋅ 10^4) — the number of test cases.

The next q lines contain test cases. The i-th test case is given as the string s consisting of at least 1 and no more than 10^5 characters 'L', 'R', 'U' and 'D' — the initial sequence of instructions.

It is guaranteed that the sum of |s| (where |s| is the length of s) does not exceed 10^5 over all test cases (∑ |s| ≤ 10^5).

Output

For each test case print the answer on it. In the first line print the maximum number of remaining instructions. In the second line print the valid sequence of remaining instructions t the robot has to perform. The moves are performed from left to right in the order of the printed sequence. If there are several answers, you can print any. If the answer is 0, you are allowed to print an empty line (but you can don't print it).

Example

Input


6
LRU
DURLDRUDRULRDURDDL
LRUDDLRUDRUL
LLLLRRRR
URDUR
LLL


Output


2
LR
14
RUURDDDDLLLUUR
12
ULDDDRRRUULL
2
LR
2
UD
0

Note

There are only two possible answers in the first test case: "LR" and "RL".

The picture corresponding to the second test case:

<image> Note that the direction of traverse does not matter 

Another correct answer to the third test case: "URDDLLLUURDR".

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.IOException;
import java.util.*;

public class SnowRobot {
	public static void main(String[] args) throws IOException {
		// current raw movements
		String raw_movements;
		
		// solution and sol length array
		int[] sol_lengths = new int[100000];
		String[] sols = new String[100000];
		
		// robot handler and 1 robot of each class
		RobotHandler robot_handler = new RobotHandler();
		BasicRobot basic_robot = new BasicRobot();
		JumpingRobot jmp_robot = new JumpingRobot();
		
		// initialize bufferedreader for fast user input
		BufferedReader user_input = new BufferedReader(new InputStreamReader(System.in));
		
		// get number of test cases
		StringTokenizer st = new StringTokenizer(user_input.readLine());
		
		// and parser it to test_cases counter
		int n = Integer.parseInt(st.nextToken());
		int c = 0;
		
		// run through specified number of test cases
		while (n-- > 0) {
			// get current movement chain
			raw_movements = user_input.readLine();
			
			// create robot according to input chain:
			// if we find a digit inside input chain...
			if ((raw_movements.length() > 1) && (raw_movements.charAt(1) == '1' || raw_movements.charAt(1) == '2')) {
				robot_handler.RobotAssign(jmp_robot, raw_movements);
			// otherwise we already know it's the basic case
			} else {
				robot_handler.RobotAssign(basic_robot, raw_movements);
			}
			
			// solve problem and add it to arraylist
			sols[c] = robot_handler.controlRobot();
			
			// get current length of solution and add it to array list
			sol_lengths[c] = robot_handler.numberOfMoves(sols[c]);
			
			// increase counter
			c++;

		}
		// print corresponding solution length with the solution after it
		for (int i = 0; i < c; i++) {
			System.out.println(sol_lengths[i]);
			System.out.println(sols[i]);
		}
		
	}

}


// Robot interface for other classes to implement
interface Robot {
	static public char[] moveset = {'R', 'L', 'U', 'D'};
	void initializeRobot();
	void  fixParity(char[] possible_moves, String movements);
	String reorderMoves();
	int getMovesLength(String move_chain);
	void Jumps2Frec();
}



// robot that can jump
class JumpingRobot implements Robot {
	// vars only useful for the jumping robot
	HashMap<Character, ArrayList<Integer>> jumps;
	HashMap<String, ArrayList<Integer>> freqs;
	
	// intialize relevant variables for jumping robot
	public void initializeRobot() {
		jumps = new HashMap<>();
		freqs = new HashMap<>();
		
		// initialize dictionary/hashmap
		for (char ch: Robot.moveset){
			ArrayList<Integer> intarr = new ArrayList<Integer>();
		
			// so we don't remain with an empty array if there are no chars of some type
			intarr.add(0);
		
			jumps.put(ch, intarr);
		}
	}
	
	// count the number of times chars appear on movements string
	// while counting jump length at the next char
	public void  fixParity(char[] all_moves, String old_moves) {
		// parse moves string into char array
		char[] moves = old_moves.toCharArray(); 
		
		// arraylists for all variables
		ArrayList<Integer>[] jmps = new ArrayList[4];
		
		// get all jump array lists
		for (int i = 0; i < all_moves.length; i++) {
			jmps[i] = jumps.get(all_moves[i]);
		}
		
		// run through all movements
		for (int i = 0; i < moves.length - 1; i++){
			// cast the next char to an int for cases like "D1L2U2..."
			int char_freq = (int) moves[i+1];
			
			for (int j = 0; j < all_moves.length; j++) {
				// add corresponding frequency of char if it's one we are looking for
				if (moves[j] == all_moves[j]) {
					// remove 0 as it's only there to fill up space if we can't find given chars
					if (jmps[j].contains(0)) {
						jmps[j].remove(0);
					}
				
					jmps[j].add(char_freq);
				}
			}
		}
		
		for (int i = 0; i < 3; i += 2) {
			// get temporary arraylists sorted in descending order
			ArrayList<Integer> temp_1 = jmps[i];
			ArrayList<Integer> temp_2 = jmps[i+1];
			Collections.sort(temp_1, Collections.reverseOrder());
			Collections.sort(temp_2, Collections.reverseOrder());
		
		
			// get sum of items in arrays
			int sum_1 = temp_1.stream().mapToInt(j -> j).sum();
			int sum_2 = temp_2.stream().mapToInt(j -> j).sum();
		
			// get difference between sum of both arrays
			int diff = Math.abs(sum_1 - sum_2);
		
			// restore parity in sum of both arrays (if odd)
			// removing 1 from it and updating sum
			if (sum_1 > sum_2 && diff % 2 != 0) {
				temp_1.remove(temp_1.indexOf(1));
				sum_1 = temp_1.stream().mapToInt(j -> j).sum();
			} else if ( sum_2 < sum_1 && diff % 2 != 0) {
				temp_2.remove(temp_2.indexOf(1));
				sum_2 = temp_2.stream().mapToInt(j -> j).sum();
			}
		
			// while both are not equal
			while ((diff = Math.abs(sum_1 - sum_2)) > 0) {
				// remove largest item from array with biggest sum
				// and update sums
				if (sum_1 > sum_2) {
					temp_1.remove(0);
					sum_1 = temp_1.stream().mapToInt(j -> j).sum();
				} else {
					temp_2.remove(0);
					sum_2 = temp_2.stream().mapToInt(j -> j).sum();
				}
			}
		
			// replace with valid jump arrays in our hashmap
			jumps.replace(all_moves[i], temp_1);
			jumps.replace(all_moves[i+1], temp_2);
		}
	}
	
	// reorder movements to valid ones after removing unnecesary ones
	public String reorderMoves() {
		// final movements
		String final_moves;
		
		// temp string array of movements
		String[] temp_moves = {"", "", "", ""};
		
		// first and second pair of atomic moves as integer array
		ArrayList<Integer> first_pair = this.freqs.get("RL");
		ArrayList<Integer> sec_pair = this.freqs.get("UD");
		
		// populate both arraylists
		//temp_pair1.add(first_pair[0]);
		//temp_pair1.add(first_pair[1]);
		//temp_pair2.add(sec_pair[0]);
		//temp_pair2.add(sec_pair[1]);
		
		// just to handle special cases:
		// if there's no up or down but there exists right and left, and also there exists an unitary move
		if ((first_pair.contains(0) && !sec_pair.contains(0)) && 
				(jumps.get('R').contains(1) && jumps.get('L').contains(1))) {
			temp_moves[0] = "R1";
			temp_moves[1] = "L1";
		// if there's no right or left but there exists up and down, and also there exists an unitary move
		} else if ((first_pair.contains(0) && !sec_pair.contains(0)) && 
				(jumps.get('U').contains(1) && jumps.get('D').contains(1))) {
			temp_moves[2] = "U1";
			temp_moves[3] = "D1";
		// otherwise (all movements are valid and exist), just add the jump lengths after the chars
		} else if (!first_pair.contains(0) && !sec_pair.contains(0)) {
			// traverse through all movements (R, L, U, D)
			for (int i = 0; i < temp_moves.length; i++) {
				ArrayList<Integer> jump_list = jumps.get(Robot.moveset[i]);
				
				// traverse trough jump list
				for (int c = 0; i < jump_list.size(); c++) {
					// get char and jump length and concat with tempmoves
					temp_moves[i] += Robot.moveset[c] + jump_list.get(c).toString();
				}
			}
		}
 		// reorder in a way it doesn't conflict with rules
		final_moves = temp_moves[0] + temp_moves[2];
		final_moves += temp_moves[1] + temp_moves[3];
		
		
		return final_moves;
	}
	
	// parse jump dictionary to a String (2 chars) -> 2 frequencies type of dict
	public void Jumps2Frec () {
		// intialize empty pair arrays
		ArrayList<Integer> first_pair = new ArrayList<>(Arrays.asList(0, 0));
		ArrayList<Integer> sec_pair = new ArrayList<>(Arrays.asList(0, 0));
		
		// run through every char associated with arraylist of ints
		for (int i = 0; i < 4; i++) {
			// get key and value
			char ch = Robot.moveset[i];
			ArrayList<Integer> jumps = this.jumps.get(ch);
			
			// get sum of jumps 
			int sum = 0;
			for (int j = 0; j < jumps.size(); j++){
				sum += jumps.get(j);
			}
			
			// put in arbitrary position according to char
			if ( ch == 'R') {
				first_pair.add(0, sum);
			} else if ( ch == 'L' ) {
				first_pair.add(1, sum);
			} else if ( ch == 'U' ) {
				sec_pair.add(0, sum);
			} else {
				sec_pair.add(1, sum);
			}
		}
		// insert our easy-to-handle arrays into frequency dictionary
		freqs.put("RL", first_pair);
		freqs.put("UD", sec_pair);
		
	}
	
	// count length of movements
	public int getMovesLength (String moves) {
		// just divide by two as every char is followed by it's jump length
		return moves.length() / 2;
	}
	
}

// basic robot (sped up implementation for codeforces)
class BasicRobot implements Robot {
	int[] freqs = new int[2];
	boolean initialized = false;
	
	// intialize relevant variables for basic robot
	public void initializeRobot() {
		if (initialized){
			return;
		}
		freqs[0] = 0;
		freqs[1] = 0;
		initialized = true;
	}
	
	// count the number of times char appears on movement string and remove 
	// necessary to end up with equal amount of 'R' with 'L' and 'U' with 'D'
	public void fixParity(char[] all_moves, String str_moves) {
		int R_or_L;
		int U_or_D;
		
		// get frequency of each one of these
		int R = 0;
		int L = 0;
		int U = 0;
		int D = 0;
		
		// char array of moves
		char[] char_moves = str_moves.toCharArray();
		
		// add 1 to frequency of given chars
		for (char ch: char_moves) {
			// basic accounting of every char
			if (ch == 'R') {
				R++;
			} else if (ch == 'L') {
				L++;
			} else if (ch == 'U') {
				U++;
			} else {
				D++;
			}
		}
		
		// get the least one between them
		R_or_L = (R > L) ? L : R;
		U_or_D = (U > D) ? D : U;
		
		// just get the frequency in there as an arraylist to complain with interface
		freqs[0] = R_or_L;
		freqs[1] = U_or_D;
		
	}
	
	// reorder moveset to a valid one after removing invalid moves
	public String reorderMoves() {
		// final string of movements
		String movements = "";
		
		// get length of R, L and D, U
		int len_R_or_L = freqs[0];
		int len_D_or_U = freqs[1];
		
		// check if there's up or down but no right or left
		if (len_R_or_L == 0 && len_D_or_U != 0) {
			movements = "UD";
		// check if there's right or left but no up or down
		} else if (len_R_or_L != 0 && len_D_or_U == 0){
			movements = "RL";
		// repeat string in a way it doesn't break the rules (done hastily as to speed up program)
		} else {
			// temporary movements as stringbuilder (is supossedly faster to work with larger inputs)
			StringBuilder temp_movements = new StringBuilder(100000);
			
			// for R
			for (int j = 0; j < len_R_or_L; j++){
				temp_movements.append("R");
			}
			// for U
			for (int j = 0; j < len_D_or_U; j++){
				temp_movements.append("U");
			}
			// for L
			for (int j = 0; j < len_R_or_L; j++){
				temp_movements.append("L");
			}
			// for D
			for (int j = 0; j < len_D_or_U; j++){
				temp_movements.append("D");
			}
			
			movements = temp_movements.toString();
		}
			
		return movements;
	}
	
	// do nothing, we don't need to for the basic robot (as to speed up our program)
	public void Jumps2Frec () {
		return;
	}
	
	// count the length of movement chain
	public int getMovesLength(String moves) {
		return moves.length();
	}
}


// main parser class
class RobotHandler {
	Robot curr_robot;
	String given_moves;
	
	// count the length of movements chain according to robot class
	int numberOfMoves(String moves_chain) {
		return curr_robot.getMovesLength(moves_chain);
	}
	
	// robot assigner for current parser
	void RobotAssign(Robot robot, String movements) {
		this.curr_robot = robot;
		this.given_moves = movements;
	}
	
	
	// make the robot fix movements and return final movement array
	String controlRobot() {
		String final_moves;
		// initialize robot
		curr_robot.initializeRobot();
		
		// fix parity in X and Y axis for R and L, and U and D
		curr_robot.fixParity(Robot.moveset, given_moves);
		
		// pass jumps and freqs to fill the last one (not useful for basic robot)
		curr_robot.Jumps2Frec();
		
		// reorder moves for robot
		final_moves = curr_robot.reorderMoves();
		return final_moves;
	}
	
 }